U.S. patent number 6,163,699 [Application Number 08/929,100] was granted by the patent office on 2000-12-19 for adaptive threshold scheme for tracking and paging mobile users.
This patent grant is currently assigned to Ramot University Authority for Applied Research and Industrial Development Ltd.. Invention is credited to Hanoch Levy, Zohar Naor.
United States Patent |
6,163,699 |
Naor , et al. |
December 19, 2000 |
Adaptive threshold scheme for tracking and paging mobile users
Abstract
A method of allocating access to a shared media network, with
specific application to tracking and paging mobile users of a
cellular telephone network. Each cell of the network broadcasts a
load factor .alpha., representative of the load on the cell's
control channel. Each user in a cell determines a registration
priority for itself, and also a registration threshold based on
.alpha.. In the preferred embodiment of the present invention, each
user is assigned a base threshold time T, and each user in a cell
computes a registration threshold time T', based on T and .alpha.,
and registers its location with the network if the last such
registration was longer ago than T'. Users are paged only in cells
to which they could have traveled since their most recent location
updates.
Inventors: |
Naor; Zohar (Tel Aviv,
IL), Levy; Hanoch (Tel Aviv, IL) |
Assignee: |
Ramot University Authority for
Applied Research and Industrial Development Ltd. (Tel Aviv,
IL)
|
Family
ID: |
25457326 |
Appl.
No.: |
08/929,100 |
Filed: |
September 15, 1997 |
Current U.S.
Class: |
455/453; 370/329;
455/405; 455/516 |
Current CPC
Class: |
H04W
74/0875 (20130101); H04W 60/04 (20130101); H04W
68/00 (20130101) |
Current International
Class: |
H04Q
7/38 (20060101); H04Q 007/00 () |
Field of
Search: |
;455/426,432,456,457,458,435,443,444,440,509 ;340/825.44
;379/113,458,426,525,526,435 ;370/332,326,338,465,522 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Tabbane, S., "An Alternative Strategy for Location Tracking",
IEEEJSAC, 13(5): 880-892 (1995). .
Madhow, et al, "Optimization of Wireless Resources for Personal
Communications Mobile Tracking", IEEE Trans. On Networking, 3(6):
698-707 (1995). .
Ho et al, "Mobile User Location Update and Paging Under Delay
Constraints", Wireless Networks, 1: 413-425 (1995). .
Rose, C., "Minimizing the Average Cost of Paging and Registration:
A Timer-Based Method", ACM J. Of Wireless Networkd, 2(2):109-116
(1996). .
Bar-Noy et al, "Mobile Users: To Update or Not to Update?",
Wireless Networkd, 1(2): 175-85 (1995). .
Rose et al, "Minimizing the Average Cost of Paging Under Delay
Constraints", ACM J. Of Wireless Networkd,1(2): 211-219 (1995).
.
Bar-Noy et al, "Tracking Mobile Users in Wireless Communications
Networks", IEEE Trans. On Information Theory, 39: 1877-1886
(1993)..
|
Primary Examiner: Bost; Dwayne D.
Assistant Examiner: Craver; Charles
Attorney, Agent or Firm: Friedman; Mark M.
Claims
What is claimed is:
1. In a shared media network including a plurality of users, a
method for allocating network resources among the users, comprising
the steps of:
(a) computing at least one load factor .alpha.; an
(b) transmitting, to each user, one of said at least one
.alpha.;
(c) for each user, computing an access threshold, based on said
.alpha. transmitted to said each user, said computing of said
access threshold being effected by said each user;
(d) for each user, computing an access priority; and
(e) for each user, accessing the network at a time depending on
said access threshold and said access priority.
2. The method of claim 1, wherein said access priority is based on
a parameter reflecting user activity.
3. The method of claim 2, wherein said parameter is selected from
the group consisting of a distance traversed since a previous
access and a time since a previous access.
4. The method of claim 1, further comprising the step of assigning
each user a certain base priority.
5. The method of claim 4, wherein said base priority includes a
base priority time T.
6. The method of claim 5, wherein said access threshold includes an
access threshold time T' based on T and .alpha..
7. The method of claim 6, wherein T' is based on a product of T and
.alpha..
8. The method of claim 6, wherein said access priority includes a
time since a previous access, said access being effected when said
time since said previous access satisfies a condition selected from
the group consisting of equaling T' and exceeding T'.
9. The method of claim 1, further comprising the step of:
(f) updating said at least one .alpha..
10. In a shared media network including a plurality of users moving
among a plurality of cells defined by boundaries, a method for
tracking the users, comprising the steps of:
(a) for each cell;
(i) computing a load factor .alpha., and
(ii) transmitting .alpha. to each user located in said each
cell;
(b) for each user, computing a registration threshold, based on
.alpha., said computing of said registration threshold being
effected by said each user;
(c) for each user, computing a registration priority; and
(d) for each users registering, with the network, an identity of a
cell whereat said each user is located, at a time depending on said
registration threshold and said registration priority, said
registering thereby constituting a location update for said each
user.
11. The method of claim 10, wherein said registration priority is
based on a user parameter selected from the group consisting of a
distance traversed since a previous location update, a number of
boundary crossings performed since a previous location update, and
a time since a previous location update.
12. The method of claim 10, further comprising the step of
assigning each user a certain base priority.
13. The method of claim 12, wherein said base priority includes a
base priority time T.
14. The method of claim 13, wherein said registration threshold
includes a registration threshold time T' based on T and
.alpha..
15. The method of claim 14, wherein T' is based on a product T and
.alpha..
16. The method of claim 14, wherein said registration priority
includes a time since a previous location update, said registering
being effected when said time since said previous location update
satisfies a condition selected from the group consisting of
equaling T' and exceeding T'.
17. The method of claim 10, further comprising the step of:
(e) for each cell: updating .alpha..
18. The method of claim 17, wherein said registering is effected
via an up-link control channel, and wherein said updating is
effected by replacing .alpha. with the product of .alpha. and a
function of U.sub.r, U.sub.c, .rho..sub.d and .rho..sub.ucc,
wherein U.sub.r is a bandwidth of said up-link control channel that
is used for said registering, U.sub.c is a bandwidth of said
up-link control channel used for call requests initiated by the
users, .rho..sub.d is a desired utilization of said up-link control
channel, and .rho..sub.ucc is an actual utilization of said up-link
control channel.
19. The method of claim 18, wherein said function is ##EQU15##
20.
20. In a shared media network including a plurality of users, a
method for allocating network resources among the users, comprising
the steps of: (a) computing at least one load factor .alpha.;
(b) transmitting, to each user, one of said at least one
.alpha.;
(c) assigning to each user a base priority that includes a base
priority time T;
(d) for each user, computing an access threshold, based on said
.alpha. transmitted to said each user, said access threshold
including an access threshold time based on T and .alpha.;
(e) for each user, computing an access priority; and
(f) for each user, accessing the network at a time depending on
said access threshold and said access priority.
21. In a shared media network including a plurality of users moving
among a plurality of cells defined by boundaries, a method for
tracking the users, comprising the steps of:
(a) for each cell:
(i) computing a load factor .alpha., and
(ii) transmitting .alpha. to each user located in said each
cell;
(b) assigning to each user a base priority that includes a base
priority time T;
(c) for each user, computing a registration threshold, based on
.alpha., said registration threshold including a registration
threshold time based on T and .alpha.;
(d) for each user, computing a registration priority; and
(e) for each user, registering, with the network, an identity of a
cell whereat said each user is located, at a time depending on said
registration threshold and said registration priority, said
registering thereby constituting a location update for said each
user.
22. In a shared media network including a plurality of users moving
among a plurality of cells defined by boundaries, a method for
tracking the users, comprising the steps of:
(a) for each cell;
(i) computing a load factor .alpha., and
(ii) transmitting .alpha. to each user located in said each
cell;
(b) for each user, computing a registration threshold, based on
.alpha.;
(c) for each user, computing a registration priority;
(d) for each user, registering, with the network, via an tip-link
control channel, an identity of a cell whereat said each user is
located, at a time depending on said registration threshold and
said registration priority, said registering thereby constituting a
location update for said each user; and
(e) updating .alpha. by replacing .alpha. with the product of
.alpha. and a function of U.sub.r, U.sub.c, .rho..sub.d and
.rho..sub.ucc, wherein U.sub.r is a bandwidth of said up-link
control channel that is used for said registering, U.sub.c is a
bandwidth of said up-link control channel used for call requests
initiated by the users, .rho..sub.d is a desired utilization of
said up-link control channel, and .rho..sub.ucc is an actual
utilization of said up-link control channel.
23. In a shared media network including a plurality of users moving
among a plurality of cells, a method for paging the users,
comprising the steps of:
(a) for each cell, providing a load factor .alpha.; and
(b) for each user;
(i) determining a personal location area, based on .alpha., by
constructing a mobility graph including a plurality of vertices,
one of said vertices being an initial vertex and at least one of
said vertices being a non-reporting vertex connected to said
initial vertex by a feasible roaming path, said personal location
area including only cells corresponding to said at least one
non-reporting vertex, and
(ii) paging said each user only in cells located in said personal
location area.
24. In a shared media network including a plurality of users moving
among a plurality of cells, a method for paging the users,
comprising the steps of:
(a) for each cell, providing a load factor .alpha.; by constructing
a mobility graph including a plurality of vertices, one of said
vertices being an initial vertex and at least one of said vertices
being a non-reporting vertex, said personal location area including
only cells corresponding to said at least one non-reporting
vertex,
(b) for each user;
(i) determining a personal location area, based on .alpha., and
(ii) paging said each user only in cells located in said personal
location area;
(c) assigning each user a base priority including a base priority
time T; and
(d) for each cell corresponding to each of said vertices, computing
a registration threshold time T' based on T and .alpha., said at
least one non-reporting vertex being defined as having a time
associated therewith that exceeds a time associated with said
initial vertex by less than T'.
25. The method of claim 24, wherein T' is based on a product of T
and .alpha..
Description
FIELD AND BACKGROUND OF THE INVENTION
The present invention relates to shared media networks, such as
cellular telephone networks, and, more particularly, to a method
for tracking and paging users of such networks.
The growing demand for Personal Communication Services (PCS)
increases the need for efficient utilization of the limited radio
resources available for wireless communication. The present
invention is concerned with the utilization of the wireless
resources devoted to location management. The problem addressed by
the present invention is the minimization of the wireless cost of
mobile user tracking in PCS networks.
The utilization of wireless network resources for mobile user
tracking has been addressed by many studies. Basically, there are
two extreme strategies that may be used for user tracking. In the
first strategy, known as "Never Update", the user never updates its
location. Thus, whenever there is a need to set up an incoming call
directed to the user, the system must search for him/her all over
the network. In the other extreme strategy, known as "Always
Update", the network continuously keeps track of the user location.
Various strategies which combine these two extremes have been
proposed in the literature. Examples of these strategies include C.
Rose and R. Yates, "Minimizing the Average Cost of Paging Under
Delay Constraints", ACM Journal of Wireless Networks, Vol. 1, No.
2, pp. 211-219, 1995; A. Bar-Noy and I. Kessler, "Tracking Mobile
Users in Wireless Networks", IEEE Trans. on Information Theory,
Vol. 39, pp. 1877-1886, November 1993; A. Bar-Noy, I. Kessler and
M. Sidi, "Mobile Users: To Update Or Not to Update?". Wireless
Networks, Vol. 1, No. 2, pp. 175-185, 1995; C. Rose, "Minimizing
the Average Cost of Paging and Registration: A Timer-Based Method",
ACM Journal of Wireless Networks, Vol. 2, No. 2, pp. 109-116, 1996;
J. Ho and I. F. Akyildiz, "Mobile User Location Update and Paging
Under Delay Constraints", Wireless Networks, Vol. 1, pp. 413-425,
1995; U. Madhow, L. Honig, and K. Steiglitz, "Optimization of
Wireless Resources for Personal Communications Mobility Tracking"
IEEE Trans. on Networking, Vol. 3, No. 6, pp. 698-707, 1995; and S.
Tabbane, "An Alternative Strategy for Location Tracking", IEEE
JSAC, Vol. 13, No. 5, pp. 880-892, 1995.
The basic idea shared by these papers is known as the "Partial
registration" strategy. Namely, upon location change a user may or
may not update its new location. The criterion for user
registration may be static, such as network partition into location
areas. For example, in the GSM system the network is partitioned
into groups of cells, referred to as location areas. A user updates
its location each time it changes a location area, while within a
location area it uses the "Never Update" strategy. Because the
partition into location areas is static, and done by the system,
not accounting for the user dynamic behavior, this strategy is
termed "static". Another type of partial registration strategy is
the dynamic strategy, in which each user decides when and where to
update its location. The criterion for user registration may be a
function of time (Rose, 1996), distance from last known location
(Bar-Noy et al. 1995; Madhow et al., 1995), number of movements
between cells (Bar-Noy et al., 1995), or based on personal location
profile (Tabbane, 1995). All the dynamic partial registration
strategies mentioned above are implemented solely on user
equipment. As such, they ignore the system activity, and depend
solely on the user activity.
The optimal solution which minimizes the user tacking cost using
these methods is of high computational complexity, and often
requires a dynamic programming method. Some of these strategies
(such as the distance based strategy) require information that is
not generally available to the user. Thus, an implementation of an
optimal solution on the user equipment is not feasible, due to
commercial, maintenance and reliability reasons. In practice, users
may register using a fixed, pre-defined parameter (timer, distance,
etc.), regardless of the exact details of user activity. Clearly,
the performance of such an implementation is inferior to the
optimal strategy. In addition, because the user decision whether to
register (update) or not to register ignores the status of other
users in the network, as well as the total load on the network, the
likelihood of collision is expected to be very high, especially at
high load periods.
There is thus a widely recognized need for, and it would be highly
advantageous to have, a method of mobile user tracking in PCS
networks that would overcome the disadvantages of presently known
methods as described above.
SUMMARY OF THE INVENTION
According to the present invention there is provided, in a shared
media network including a plurality of users, a method for
allocating network resources among the users, including the steps
of: (a) computing at least one load factor .alpha.; (b)
transmitting, to each user, one of the at least one .alpha.; (c)
for each user, computing an access threshold, based on the .alpha.
transmitted to the each user; (d) for each user, computing an
access priority; and (e) for each user, accessing the network at a
time depending on the access threshold and the access priority.
According to the present invention there is provided, in a shared
media network including a plurality of users moving among a
plurality of cells defined by boundaries, a method for tracking the
users, including the steps of: (a) for each cell: (i) computing a
load factor .alpha., and (ii) transmitting .alpha. to each user
located in the each cell; (b) for each user, computing a
registration threshold, based on .alpha.; (c) for each user,
computing a registration priority; and (d) for each user,
registering, with the network, an identity of a cell whereat the
each user is located, at a time depending on the registration
threshold and the registration priority, the registering thereby
constituting a location update for the each user.
According to the present invention there is provided, in a shared
media network including a plurality of users moving among a
plurality of cells, a method for paging the users, including the
steps of: (a) for each cell, providing a load factor .alpha.; and
(b) for each user: (i) determining a personal location area, based
on .alpha., and (ii) paging the each user only in cells located in
the personal location area.
Recognizing the drawbacks of the prior art methods, the present
invention shifts a significant part of the tracking activity from
the user's equipment to the system's equipment, and integrates more
intelligence on the network side. The basic idea is to leave user
specific decisions in the user's equipment while moving network
general decisions to the network. Guided by this basic idea, the
present invention uses a novel approach for mobile user tracking,
in which the registration of a user is based not only on its own
activity, but also on local network load and the status of other
users within the same cell.
The implementation of this approach is achieved via the following
mechanism: A user computes its registration priority based on its
own activity. On the other hand the network determines, for each
cell, a load factor, based on cell load, time of day, day of week,
etc. This parameter, which is unique for each cell, is transmitted
by each base station, as a broadcast message to all the users
within the cell, through the down link control channel. Finally,
the decision of when to transmit a registration message is done by
the user but is based on both parameters: Such a message is sent
whenever the user's registration priority exceeds a local
registration threshold level based on the cell's load factor.
The advantage of the present invention over other methods is in
taking into account the system activity: Less critical registration
messages are avoided during heavy traffic periods, while low
traffic periods and areas are used to gather extensive information
on user locations. Fukumine et al., in U.S. Pat. No. 5,212,822,
present a registration method for a mobile communication system in
which, as in the present invention, the users' decisions whether to
register are based on information received from the base stations;
but that information is static information that relates to the
geometry of the system. In the present invention, the information
broadcast to the users reflects the dynamic load of each cell.
In its most general form, the adaptive threshold scheme of the
present invention is a method for allocating access to shared media
networks in general. Examples of shared media network accesses to
which this adaptive threshold concept is applicable include
accesses of shared data bases, routing in large networks, and
access in X-protocol based networks. Load sensitive algorithms, in
many areas, are implemented either by a central approach, in which
system resources are allocated to the users by the system, or by a
distributed approach, in which each user makes its own decisions,
using an agreed upon Media Access Control protocol. The adaptive
threshold approach of the present invention suggests another way:
Due to the huge number of users in a PCS network, the media access
algorithm (i.e. the registration) must be distributed, where each
user makes its own decision when and where to update its location.
On the other hand, to reduce the likelihood of collision, and
improve system performance, the network informs the users about the
cost of registration.
The present invention has two aspects:
1. An access algorithm, based on a dynamic threshold, which is
sensitive both to the user activity and to the system load.
2. In a PCS network, an efficient paging algorithm which takes
advantage of the dynamic thresholds used by the access
(registration) strategy.
Although the present invention is applicable to shared media
networks in general, the focus of the detailed description below is
on the specific application of the present invention to tracking
and paging users in a PCS network. In the context of a PCS network,
the system load is the load on the cells of the system. In the
context of shared media networks in general, the correspondences of
the components of a specific type of shared media network to the
components of a PCS network will be transparent to those ordinarily
skilled in the art. For example, in a shared data base, the data
base itself can be treated as a single large cell; and in the
routing problem, each node of the network corresponds to one cell.
Whenever the term "registration" is used herein, it will be
transparent to those ordinarily skilled in the art what the
corresponding access mode is in any given shared media network.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention is herein described, by way of example only, with
reference to the accompanying drawings, wherein:
FIG. 1 shows the topology of a model system for analyzing the
present invention;
FIG. 2 contains plots of the uncertainty of user location vs.
distance between highly loaded areas;
FIG. 3 contains plots of the uncertainty of user location vs.
threshold distance.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
The present invention is of a method for tracking and paging mobile
users of a shared media network. Specifically, the present
invention can be used to track and page the users of a PCS
network.
The principles and operation of user tracking and paging according
to the present invention may be better understood with reference to
the drawings and the accompanying description.
Consider a wireless network partitioned into cells. The network is
assumed to be large enough, so that the expected number of users is
constant, and assumed to be mitch larger than the number of radio
channels. To a good approximation, the number of users may be
considered as infinite, for traffic considerations. The user
location is understood as an identifier of a cell in which the user
is currently residing. Two cells are called neighboring cells if a
user can move from each one of them to the other, without crossing
any other cell. To model user movement in the network it is assumed
that time is slotted, and that a user can make at most one cell
transition during a slot. It is assumed that the movement of the
user is done only at the beginning of a time slot, such that the
movement precedes any other event, such as a paging event. The
movements are assumed to be stochastic and independent from one
user to another. It is assumed that calls are initiated by the
users as a Poisson process at average rate .lambda.. The user
roaming interval is defined as in Rose (1996), as the time interval
since the last contact of a user with the system, and the next
paging event to this user.
The tracking algorithm is split between the user and the network.
The registration algorithm performed by the user is based on the
user activity and on the load factor, computed by the network. Each
cell computes its own load factor, independent of the other cells,
and announces it to the users as a broadcast message, through the
down link control channel. In addition, each user computes its own
registration priority. Preferably, the user's registration priority
is based on its current foaming interval, defined as the length of
time since the last time it contacted the system to notify the
system of its location; although the scope of the present invention
includes priorities based on other dynamic user parameters, such as
the distances traveled by the user since the user's last contact
with the system or the number of cell boundary crossings performed
by the user since the user's last contact with the system. The user
also computes a local registration threshold time, based on the
local load factor. Although in general the user registration
priority may be any monotonic function of the user's Current
roaming interval, in the embodiment of the present invention
presented herein the user registration priority is identical to the
user's current roaming interval. Whenever the user registration
priority exceeds the local registration threshold time, the user
transmits a location update message. Because the local load factor
depends on the current load on the cell, different cells may have
different load factors.
The search algorithm at a paging event is restricted only to the
set of all possible user locations. Namely, all the cells that
satisfy two conditions: 1) The user's registration threshold time
in those cells at the paging event is higher than the user roaming
interval, say t, and, 2) The cells are reachable from the user last
known location within t steps, without sending a registration
message on the way.
The user registration strategy is based on a timer-based approach
(Rose, 1996). In the preferred embodiment of the present invention
described herein, the user attempts to transmit an update message
every T' time units, where the parameter T' is not fixed, but
depends on the current signaling load at the user location. The
parameter T', referred to as the local registration threshold time,
is evaluated by the user using T'=T.alpha., where T is a fixed,
pre-defined base priority time, unique for the user, and .alpha. is
the local load factor, transmitted by each base station as a
broadcast message, through its down link control channel (DCCH, in
the GSM system). The dynamic parameter .alpha. reflects the current
local load on the control channel, thus it may vary from cell to
cell. The load factor of a cell i is denoted by .alpha.(i). The
user will transmit a registration message whenever:
where time is measured in units of time slots, where t is the user
current roaming interval and where i is the user current
location.
Each cell in the network computes its current load factor,
independently of the other cells. The load factor is transmitted by
the cell, as a broadcast message, through the clown link control
channel. Because registration messages are transmitted through the
up link control channel (UCC), the main concern is to guarantee
that an increase in the registration activity will not jam the
UCC.
The basic idea is the following: Let .rho..sub.ucc be the fraction
of the UCC bandwidth used by a cell, 0.ltoreq..rho..sub.ucc
.ltoreq.1. Whenever .rho..sub.ucc drops below a pre-defined
threshold, say .rho..sub.L, the load factor .alpha. decreases. As a
result, the activity of location update operation (registration)
increases on lightly loaded cells. On the other hand, whenever
.rho..sub.ucc exceeds (another) pre-defined threshold, say
.rho..sub.H (.rho..sub.H >.rho..sub.L), the load factor
increases. To stabilize the algorithm, the modification rate of the
load factor follows a hysteresis curve.
Load Factor Modification Algorithm
Because the UCC is used for call handling requests and registration
messages initiated by the users, the actual use of UCC resource,
denoted by U.sub.ucc is given by:
where U.sub.r is the bandwidth actually used for registration, and
U.sub.c is the bandwidth used for the call requests initiated by
the users. In reality, the registration threshold time T' is
significantly smaller than the reciprocal of the call rate:
T'<<1/.lambda.. Thus, the registration rate is, for a good
approximation, given simply by 1/T', implying that it is linear
with 1/.alpha.. Therefore, given a UCC utilization .rho..sub.ucc,
the new value of the load factor, denoted by .alpha.', required to
obtain a desired UCC utilization .rho..sub.d, is given by: ##EQU1##
Solving for .alpha.' gives: ##EQU2## A reasonable choice of the
desired UCC utilization .rho..sub.d is: .rho..sub.d =(.rho..sub.L
+.rho..sub.H)/2. Thus, the modification rate of the load factor
.alpha. should be a function of the UCC utilization, .rho..sub.ucc,
the current bandwidth used for registration, U.sub.r, and the
thresholds .rho..sub.L and .rho..sub.H. To ensure the stability of
the load factor, the size of the time interval required to evaluate
the next value of the load factor should be long enough to avoid
statistical fluctuations. Preferably it is significantly longer
than the time slot used for registration.
The Paging Algorithm
Consider a paging event at time t=.tau.. for a user u with roaming
interval equal to .tau., whose last known location, at time t=0, is
X.sub.0. The distance between two cells, say x and y, denoted by
d(x,y), is defined as the length of the shortest path between x and
y, measured in number of cells. Notice that d(x,x)=0, and that
d(xy)=1 if and only if x is a nearest neighbor of y.
The goal is to minimize the number of locations at which the user
is paged.
Definition: The mobility graph G is defined as a directed graph, in
which all vertices are of the form (x,t) where x is a cell in the
network, and t is a time slot. Note that x and t are integers. A
(directed) edge exists between two vertices, say (x.sub.1,t.sub.1)
and (x.sub.2,t.sub.2). in the mobility graph if and only if: 1)
d(x.sub.1,x.sub.2).ltoreq.1, and 2) t.sub.2 =t.sub.1 +1. Notice
that there are two different types of edges in the mobility
graph:
A static edge is a directed edge from the vertex (x,t) to the
vertex (x,t+1), reflecting a situation where the user remains at
its last location.
A dynamic edge is a directed edge from the vertex (x.sub.1,t) to
the vertex (x.sub.2,t+1), where x.sub.1 and x.sub.2 are nearest
neighbors, reflecting a user motion from cell x.sub.1 into cell
x.sub.2, at time t+1.
Definition: A non-reporting (NR) vertex is a vertex (x,t) in the
mobility graph satisfying both conditions:
A Non-Reporting vertex represents a point (in time and space) which
is reachable from the user last known location during its roaming
interval, and in which the user should not transmit a registration
message.
Note that because distance is measured in number of cells, and time
is measured in time slots, distance is commensurate with time,
using the assumption that a user can make at most one cell
transition during a single time slot. This assumption can become
reality by properly choosing the size of the time slot, such that a
user can not cross more than one cell during a single time slot.
For example, a user moving at a velocity of 6 km/h can move at most
100 meter in one minute.
Note that (X.sub.0,0) is always a NR vertex, because
.alpha.(x,t)T>0; for all x and t, and d(x,x)=0 for all x.
A feasible roaming path is defined as a directed path in the
mobility graph, which starts at (X.sub.0,0), and for which all the
vertices in the path are NR vertices. Given that the roaming
interval of u is equal to .tau., its actual roaming path must be a
flesible roaming path in length .tau., starting at (X.sub.0,0) and
terminating at the user location at time .tau..
Definition: The personal location area (PLA) of u at time .tau., is
defined as the set of all cells, x, such that the vertex (x,.tau.)
in the mobility graph is a non-reporting vertex, and is connected
to the vertex (X.sub.0,0) through a roaming path.
Lemma 1: Let x be the location of a user u at time t=.tau.. Then, x
is a member of the PLA of u.
The proof is given in appendix A.
Lemma 2: The PLA of u is the minimal set of cells, satisfying the
condition that paging u in all cells within the set must locate
u.
The proof is given in appendix B.
The meaning of Lemmas 1 and 2 is that the PLA of u is the minimal
set of locations at which paging u guarantees a success.
The paging algorithm is subject to one-phase paging delay: When a
paging event occurs, the user is paged simultaneously in all the
cells belonging to the PLA.
The first step of the paging algorithm is to find all cells
belonging to the PLA of u. The algorithm uses a Breadth First
Search (BFS) on the mobility graph, beginning from the vertex
(X.sub.0,0), which represents the user last known location,
X.sub.0, at time t=0. The BFS is conducted in steps, where the k-th
step accepts as an input a set, A(k-1), produced by the (k-1) step,
and generates the set A(k). A(k) is the set of NR vertices of the
form (x,k), connected to the vertex (X.sub.0,0) through a feasible
roaming path. For each member in A(k-1), say (x,k-1), in the k-th
step all vertices of the form (x',k) are considered, where x' is
either x or a nearest neighbor of x. If (x',k) is a NR vertex, it
is added to the set A(k). In the first step A(0) contains the
vertex (X.sub.0,0), and the nearest neighbors of X.sub.0 are
considered at time slot t=1. The search is terminated when either
k=.tau.+1, or the set A(k) is empty.
Proposition: The set of all cells x, such that (x,.tau.).di-elect
cons.A(.tau.) is the PLA of u. Namely, A(.tau.) contains all NR
vertices of the form (x,.tau.), connected to (X.sub.0,0) through a
feasible roaming path.
The proposition can be proved by induction on k that shows that
A(k) is the set of all NR vertices of the form (x,k), connected to
(X.sub.0,0) through a feasible roaming path in length k. Thus,
A(.tau.) is the set of all NR vertices of the form (x,.tau.),
connected to (X.sub.0,0) through a feasible roaming path.
To construct the PLA of u the system keeps, for each cell, a table
of its load factor .alpha., as a function of time. In addition, the
mobility graph is based on the adjacency graph of the network.
Because the BFS is conducted on both time and space, the nearest
neighbors of X.sub.0 can be visited in the worst case .tau. times,
while the cells in a distance .tau. from X.sub.0 are visited at
most one time. Recalling that a user can make at most one cell
transition during a time slot, distance is commensurate with time.
Let n(X.sub.0,j) be the number of cells within a distance less or
equal to j from X.sub.0, where n(X.sub.0,0)=1. In the i-th
iteration of the BFS algorithm, at most n(X.sub.0,i) vertices are
considered. An upper bound on the worst case complexity of the BFS
algorithm is given by: ##EQU3## In reality, the number of nearest
neighbors of a cell is bounded by some constant, and so is the
density of cells per area unit. Thus, the maximal number of cells
reachable within t time-slots is O(t.sup.2), and the worst case
complexity of the BFS algorithm is therefore: ##EQU4## The
explanation of the computational complexity is that the BFS on the
mobility graph searches in O(.tau..sup.2) cells, each cell has at
most .tau. vertices, yielding O(.tau..sup.3) vertices, and
therefore O(.tau..sup.3) edges.
Lemma 3: If the number of cells reachable within t time slots is
.OMEGA.(t.sup.2), then the construction of the PLA has a worst case
complexity of .OMEGA.(t.sup.3).
The proof is given in appendix C.
Note that the process which finds all members of the PLA is a
computational task. As such, it makes no use of wireless network
resources. The search is done on the mobility graph, not on the
network's physical infrastructure.
In practice, the load distribution over the network changes
gradually, relative to user motion. Thus, the load factor is
expected to change only every k time slots, where k is a constant.
The number of iterations required can be reduced to x=[.tau./k]+1,
where in each iteration the BFS is extended by a distance k. The
worst case complexity, under this assumption becomes: S=O(k.sup.2
x.sup.3), which is proportional to .tau..sup.3 /k. This is still
O(.tau..sup.3), but the computational task is reduced by a factor
k. Consider for example a user with average velocity of 6 km/h
within a two-dimensional mesh topology of cells in dimensions of
100 m.times.100 m for each cell. A proper choice of a time slot is
1 minute, while the update rate of the load factor may be every 10
minutes, yielding k=10.
In practice, the local load in each cell is not expected to vary
significantly during a single roaming interval. For example, if the
maximal registration threshold time for any user is approximately
15 minutes and the load factors are updated every 10 minutes, then
for most cells the local registration threshold time is not
expected to change during the user's roaming interval. Thus, the
registration threshold time is expected to change very slowly
within the user roaming interval. Assuming:
.alpha.(x,0).apprxeq..alpha.(x,.tau.). .A-inverted.x there is no
need for .tau. iterations. Under this assumption, the BFS can be
conducted only on vertices of the form (x,.tau.) in one
iteration.
Consider a user u whose last known location is X.sub.0, at time 0.
If a paging event occurs at time .tau., then a search is conducted
simultaneously in all the members of A(.tau.). Because the search
is conducted in one phase, the paging delay is minimal. On the
other hand, the cost of paging, in terms of number of locations
that must be searched is relatively high.
Performance Analysis
In general, a dynamic registration threshold time parameter is more
efficient than a static one, for the following reasoning: Let
T.sub.s be a static registration threshold time. The dynamic
parameter T' in location i at time t is given simply by: T'=T.sub.s
.alpha.(i,t). Whenever T'<T.sub.s, it implies that there are
non-utilized wireless resources in the UCC of cell i, at time t, to
be used by the system to reduce the expected paging cost, without
inflicting any degradation on system performance. In other words:
without increasing the actual cost of registration. On the other
hand, a situation where T'>T.sub.s implies that the UCC is
overloaded. In practice, such cells are split to prevent
undesirable grade of service. Therefore this situation is expected
to exist only for short time periods, in a small fraction of the
network. Minimizing the registration activity during these epochs
should guarantee the quality of service provided by the network,
without increasing significantly the uncertainty in user
location.
The question which remains open is the quantification of the
differences in the tracking cost between static and dynamic
registration threshold time parameters. In general, the efficiency
of the ATS method, relative to other dynamic strategies, depends on
the exact details of the network topology, the load distribution on
the network, and the users mobility and call pattern. Moreover,
because the load factor may vary from one cell to another, and
depends on both location and time, the cost of paging a user
depends also on its traveling path.
Let F(x,t) be the expected cost of paging a user at time t, given
that its last known location is x, at time 0. Implicit in the (x,t)
notation is the assumption that the distribution of user location
at time t>0 depends only on its location at t=0. For the sake of
simplicity this notation is retained herein, with the understanding
that it may be extended in the future. The expected cost of paging
a user whose last known location is x is then given by: ##EQU5##
where P(t) is the probability that the user roaming interval is
terminated by a paging event at time t. The expected cost of paging
the user is then: ##EQU6## where .eta.(x) is the probability that
the user last known location is x. It should be noted that .eta.(x)
is not necessarily the steady state probability of being in
location x. The reason is the dependency of .eta.(x) on the
registration process, which is itself dependent on user location.
For example, crossing a lightly loaded cell, even for a short
period of time, will produce a registration message, while residing
within a highly loaded cell will cause registration only if the
user roaming interval exceeds the local registration threshold
time, which is expected to be relatively high.
In order to relate the performance of the ATS strategy to the
steady state location probability distribution, the concept of the
potential uncertainty in location, induced by the ATS strategy on
the network, is used. This location uncertainty provides an upper
bound on the paging cost. Let .phi.(x,.tau.) be the number of cells
belonging to the PLA of a user whose location at time 0 is x, at
time .tau., given that no location update occurred in [0,.tau.].
The potential uncertainty of u is defined as: ##EQU7## where
.theta.(x,.tau.) is the probability that the roaming interval is in
length .tau., given that the location is x. An upper bound on the
paging cost is given by: ##EQU8## where q(x) is the probability
that the user location at time 0 is x. Because user motion and
paging are assumed independent processes, q(x) is equal to
.pi..sub.x, the steady state probability of being in location
x.
Equation (10) provides the expected cost of one-phase paging under
the ATS strategy, because all the cells in the PLA are paged
simultaneously. The static registration threshold time method can
be derived as a special case of the ATS strategy, for homogeneous
load distribution. In this situation, .phi.(x,.tau.) is simply all
cells in a distance not larger than .tau. cells from the user last
known location, and all local registration threshold times have the
same value, say T. Because in reality the load distribution is
never homogeneous, the value of T must be derived from the load on
the most loaded cells. The paging cost under the static
registration threshold time method can be derived from Equation
(10) by substituting .DELTA.(x) by a constant T'. Following the
reasoning stated above, the static registration threshold time T is
always greater or equal than a dynamic registration threshold time,
thus, the paging cost of the static registration threshold time
method is always greater than the paging cost of the AFS strategy.
In the extreme case of homogeneous load distribution the ATS
strategy yields the same performance as the static registration
threshold time method. The other extreme situation is when most of
the users concentrate in relatively small number of cells, such
that all loaded areas in the network are isolated cells, surrounded
by lightly loaded cells, where any transition from one loaded cell
to another must cross a series of lightly loaded cells. In this
case, the PLA of all users is minimal, even if they transmit
registration messages very rarely.
To demonstrate the ATS performance, a system consisting of an
infinite chain of highly loaded (HL) areas, connected together
through lightly loaded cells, is considered. Neighboring HL areas
are separated by a line of D lightly loaded cells. FIG. 1 shows an
example of the model, for D=5. The user motion model is a random
walk. To model the user movement it is assumed that time is
slotted, and a user can make at most one move during a slot. The
users movements are assumed to be stochastic and independent from
one user to another.
An application that can be modeled by such a system is a group of
highly loaded areas such as shopping centers, campuses, or
buildings, connected through a highway, or a main road. Each two
neighboring HL areas 10 are connected together through a
one-dimensional line 20 of D lightly loaded cells 25, where the
local registration threshold time in each lightly loaded cell 25 is
T.sub.L. Within HL area 10, the user motion model is a random walk:
A user located in each cell 15 of HL area 10 can move out of HL
area 10 or remain in HL area 10. Upon entering a lightly loaded
cell 25, the user motion model is also a random walk.
Let T be the local registration threshold time under the static
method. Under the ATS strategy there are two local registration
threshold times in the system: a relatively long registration
threshold time T.sub.H in HL areas 10, and a relatively short
registration threshold time T.sub.L in lightly loaded areas 20.
Following the reasoning stated above, choose T.sub.H =T>T.sub.L.
The main advantage of the ATS strategy over the static method lies
in the ability of the ATS to increase the registration rate in
lightly loaded areas 20. For example, if any attempt to move from
one HL area 10 to another must yield a registration message
(somewhere along the transition line), then given that the user
last known location is inside an HL area 10, its PLA contains no
more than one HL area 10. In contrast, using a static method, a
search must be conducted, in general, in more than one HL area 10.
This model captures the main advantage of the ATS strategy over a
static method: if a transition from one highly loaded area to
another must cross a lightly loaded cell, a registration message
must be transmitted. This update message significantly reduces the
future paging cost, without increasing the actual wireless cost of
registration.
Clearly, the ATS strategy outperforms the static method within
lightly loaded areas 20. However, the problem of reducing the
trackings cost is crucial only in HL areas 10. Therefore, the
present analysis will concentrate only in evaluating the cost of
tracking in those areas. This value is referred to herein as the
actual tracking Cost. The registration cost in these cells is
identical in both methods, because they both use the same
registration threshold time T.
The paging cost is bounded by the number of cells within the
personal location area (PLA) of the user. What is of interest is
the number of cells within the PLA. Define the threshold distance,
denoted by D*, as the maximal number of cells a user can travel
within a lightly loaded area without transmitting a registration
message. Recalling that a user can make at most one cell transition
in a single time slot, it follows that under the ATS strategy
D.sub.ATS =T.sub.L -1, while under the static method D*.sub.static
=T-1. Let .vertline.PLA(.tau.).vertline. be the size of the PLA of
a user having a roaming interval equal to .tau., measured in number
of HL areas within the PLA. Recall that D is the distance between
neighboring HL areas, expressed in terms of number of cells.
Then:
Proposition: Under the ATS strategy, an upper bound on the size of
the PLA, for any given value of .tau., is given by: ##EQU9##
Proof: Let x be the user last known location. The user can enter an
HL area without transmitting a registration message only if its
distance from x is at most D*+1, in each direction. Thus, the upper
bound on the PLA size is the maximal number of HL areas within an
interval in a length of [2(D*+1)], which is ##EQU10##
Thus, the uncertainty in user location, and therefore the paging
cost increases with D*/D: The lower the load on the neighbors of
the highly loaded cells, or the larger the distance between two HL
cells, the lower the paging cost, as expected. Therefore, the
isolation factor of the loaded areas is defined herein as the ratio
D*/D.
Note that for T.sub.L =1, D*=0, yielding an infinite isolation
factor. In this situation, the user location within the lightly
loaded area is known precisely.
Using the static method, the PLA size, .vertline.PLA.vertline.,
measured in the number of HL areas, is obtained by substituting
D*.sub.static =T-1 in Equation (11): ##EQU11## for any given value
of .tau..
The performance of the ATS strategy now will be compared to the
static method, using the above worst-case scenario. Subtracting
Equation 11 from Equation 12 demonstrates that the upper bound on
the size of the PLA under the static method is greater than the
upper bound on the size of the PLA under the ATS strategy by
##EQU12## areas. Thus, the ATS strategy outperforms the static
method, and the difference in the performance is, to a good
approximation, proportional to the ratio ##EQU13## This difference
increases with T-T.sub.L, which reflects the load variability
between highly and lightly loaded cells, and decreases with the
distance D. If D.gtoreq.2T then .vertline.PLA.vertline..ltoreq.1
for both strategies, implying that if the distance between
neighboring HL areas is large enough, a dynamic threshold time
would reduce the paging cost only in the lightly loaded areas. The
dependence of the benefit of the ATS strategy on T-T.sub.L implies
that even a relatively small reduction in the local registration
threshold in the lightly loaded cells, relative to the local
registration threshold in the heavily loaded cells, may reduce
significantly the paging cost. Consider, for example, a system in
which T=20, T.sub.L =16, and D=2. Under the static method the PLA
may contain, in the worst case, up to 14 HL areas, compared to at
most 11 HL areas under the ATS strategy. Recalling that under the
static method most of UCC resources are under-utilized (for most
locations), the saving in paging cost is expected to be
significant.
The performance of the ATS strategy is illustrated in FIGS. 2 and
3.
FIG. 2 depicts the upper bound on the number of rings contained by
the PLA, given in Equation 11 for the ATS strategy, and in Equation
12 for the static method, as a function of the distance D between
two highly loaded areas. The ATS strategy outperforms the static
method, and the difference in the performance of both methods
decreases with the distance D, as expected. FIG. 3 demonstrates the
dependence of the upper bound on the PLA size, on the threshold
distance D*.sub.ATS. In the system illustrated, D=1 and T=20. The
ATS strategy outperforms the static method, where optimal
performance is achieved for minimal T.sub.L, as expected. Both
Figures depicts the dependency of the superiority of the ATS
strategy on the static method as a function of the ratio
##EQU14##
Appendix A: Proof of Lemma 1
Let x be the location of u at time .tau.. Because u did not
register at .tau., .alpha.(x,.tau.)>.tau./T. Thus, (x,.tau.) is
a NR vertex. Because u did not register during the time interval
[0,.tau.], its traveling path from X.sub.0 to x must form a
feasible roaming path. Thus, x is a member of the PLA of u.
Appendix B: Proof of Lemma 2
Let x be a member in the PLA of u. From the definition of the PLA,
there is a feasible roaming path from (X.sub.0,0) to (x,.tau.).
Because the user can move from each cell to each one of its nearest
neighbors, there is a sequence of time intervals, say [0,t.sub.0 ],
[t.sub.0 +1,t.sub.1 ], . . . [t.sub.1 +1, .tau.], in which lit
could pass from X.sub.0 to x without transmitting a registration
message. Thus, the probability that the location of u at time .tau.
is x, is greater than 0. Therefore, u must be paged in x.
Appendix C: Proof of Lemma 3
Consider a two-dimensional grid system, where the user's local
registration threshold time in each cell changes randomly every
time slot, such that the local registration threshold time can take
any integer value in the interval [1,.tau.], with equal probability
for each value. In every time slot, the user can move, with equal
probability, to each one of its 8 nearest neighbors. Thus, the
number of cells reachable within .tau. time slots is
.OMEGA.(.tau..sup.2), meaning that after .tau. steps there are
.OMEGA.(.tau..sup.2) candidates for the user location at time
.tau.. A cell x is a member in the PLA if and only if there exists
at least one feasible roaming interval in length .tau., describing
the user locations at time t=0,1,2, . . . .tau.. Thus, given a cell
x, the verification that x .di-elect cons.PLA has a computational
complexity of .OMEGA.(.tau.), because exactly .tau. vertices in the
mobility graph must be verified. Because the size of the PLA is
.OMEGA.(.tau..sup.2), its verification required
.OMEGA.(.tau..sup.3) steps. Thus, constructing the PLA must has a
computational complexity of .OMEGA.(.tau..sup.3).
While the invention has been described with respect to a limited
number of embodiments, it will be appreciated that many variations,
modifications and other applications of the invention may be
made.
* * * * *